But he faced fresh embarrassment last night after the publication by the Leveson inquiry, into press standards, of hundreds of text messages exchanged between senior Government advisers and insiders at the tycoon’s News Corporation.

In an indication of the astonishing familiarity between senior Tories and the media giant, one message showed Mr Hunt addressing a lobbyist representing News Corp, as “daddy” and “papa”.

Mr Cameron yesterday dismissed growing calls for Mr Hunt’s sacking over allegations that he was too close to the company he was supposed to be overseeing in a “quasi-judicial” capacity. “I don’t regret giving the job to Jeremy Hunt. It was the right thing to do under the circumstances,” Mr Cameron said.

There was no great conspiracy

David Cameron

The row intensified following the emergence of a memo sent by Mr Hunt to the Prime Minister expressing enthusiastic support for the News Corp bid before he was given the job of deciding on the issue.

Mr Cameron insisted Mr Hunt had acted impartially. “There was no great conspiracy,” he added.

A 37-year-old woman journalist on The Sun was arrested yesterday as part of Scotland Yard’s Operation Elveden inquiry into alleged payments to public officials. She is the 30th suspect in the probe.